MK Dons and Peterborough's promotion parties remain on hold while Hereford stay third in League Two.
MK Dons and Posh would have secured League One football next term with wins, but slipped up at home to Wycombe and Stockport respectively.
Paul Ince's side needed an injury-time effort from Sean O'Hanlon to rescue a 2-2 stalemate with Wycombe, while Stockport won 1-0 at Peterborough.
The Hatters stay just outside the automatic promotion places following Hereford's crucial 1-0 victory over out-of-sorts Darlington.Second from bottom Mansfield remains four points adrift of Dagenham & Redbridge with both sides drawing.
See below for match summaries:
Barnet have climbed above Bury in the table following a 3-0 win at Underhill. The game was goalless at half-time but The Bees cut loose after the interval. Adam Birchall's brace set Barnet on their way before Cliff Akurang's late effort added the icing on the cake.
All the goals arrived early on at Griffin Park as Brentford and Bradford shared the spoils in a 2-2 draw. Goals from Peter Thorne and Kyle Nix put The Bantams in front after Glenn Poole opened the scoring early on. Alan Bennett's 26th minute strike for Brentford was the end of the scoring.
Lincoln City beat Chester 2-1 despite playing out the last 20 minutes a man light. Things looked good for Chester early on when Paul McManus opened the scoring after 20 minutes. However, a quick-fire brace from Jamie Forrester gave the Red Imps a half-time lead. The visitors had to see out the closing stages a man down after Danny N'Guessan collected his second yellow card of the game.
Dagenham & Redbridge remain four points clear of second from bottom Mansfield after coming from a goal down to draw 1-1 at the Glyn Hopkin Stadium. Kallum Higginbotham gave Rochdale the lead on 28 minutes, but it was short-lived after Ben Strevens' effort just five minutes later secured a point for the home side.
Darlington's automatic promotion hopes are fading fast following yet another defeat. Despite an evenly-contested match in the North East, Gary Hooper's 69th minute effort secured the points for The Bulls. The result leaves Darlington four points adrift of Hereford, who also have two games in hand.
Ryan Taylor netted the only goal of the game as Rotherham secured a 1-0 win at Grimsby. Taylor's effort, which came five minutes before half-time, lifted The Millers over Grimsby in the League Two table.
Mansfield failed to improve their hopes of avoiding the drop despite picking up a point away from home. A win over their fellow strugglers could have moved The Stags to within two points of third from bottom Dagenham & Redbridge.
MK Dons missed the chance to win promotion to League One on Saturday despite claiming a late point at home to Wycombe. Scott McGleish bagged a brace for Wycombe, but it was not enough to secure all three points courtesy of O'Hanlon's effort deep into injury-time. Aaron Wilbraham's close-range effort briefly restored parity prior to McGleish's second.
Chesterfield's hopes of making the play-offs were hindered after being held to a 1-1 draw at Morecambe. Steve Fletcher's effort looked like claiming the points for The Spireites until Matthew Blinkhorn's 74th minute leveller.
Notts County boosted their hopes of avoiding the drop following a crucial 1-0 success over Accrington Stanley. Ryan Jarvis' 37th minute goal was enough to secure all three points for The Magpies.
Stockport maintained the pressure on Hereford for the final automatic promotion place in League Two with a superb 1-0 away win at Peterborough. A win for Posh would have secured League One football for next season, but Tommy Rowe's goal a minute before the hour mark was enough to delay Peterborough's promotion party.